This study uses a concept of interval differentiability, which was recently introduced, to formulate interval initial value problems involving linear interval differential equations. Differently from the approaches that use the gH-differentiability, this study does not make use of a criterion of choice for switching points in order to obtain solutions for such problems. The method herein presented provides solutions in a simple, straightforward, and computationally tractable way. Moreover, these solutions are intuitive because they coincide with the solutions given by a differential inclusion method. The efficiency and practicality of our approach are illustrated through some examples that have appeared in other articles.